两个变量之间的独立性检验是统计推断中基本的检验之一。如果两个变量是一维的，很多文献采用一维情况下独立性检验统计量作为特征筛选指标。如果两个变量的维数是高维的，也有一些相关的研究。不同于已有的文献研究，本课题提出了几种独立性检验的方法，主要的研究内容包括：1. 在两个变量是一维的情况下，对于任意两个变量，提出通过样本分割，基于二分类独立性检验得到的统计量，构造最终统计量。并且提出把高维独立性检验问题通过投影方法降维，构造统计量；2. 对于高维变量独立性检验，基于空间分割的方法，提出统计量，研究统计量在原假设和备择假设下的性质；3. 提出高维空间下，数据秩的定义，构造基于秩统计量的高维独立性检验统计量；4. 提出基于最小生成树的高维独立性检验统计量，并且研究其相关性质。对于提出的高维独立性检验统计量，研究不同统计量在不同相关情况下，以及在维数和样本量不同情况下，统计量的有效性及其应用。

Independence test for two random variables is one of the basic tests in statistical inference. If both of two variables are one-dimensional, many literatures apply independence test statistics as feature screening indicators. If the random variables are high-dimensional, there are also some related investigation. Different from the existed statistics for independent test, this project proposes several methods for independence test. The research mainly includes: 1. In the case that two variables are one-dimensional, we first cut the data into two-class by any cutpoint from sample. The statistics is constructed from sample segmentation for each cutpoint and obtain the final statistics. Also, we propose to reduce the high-dimensional data by projection method and construct the corresponding statistics; 2. For high-dimensional independence test, we propose statistics based on spatial segmentation method, and study the properties of statistics under null and alternative hypothesis; 3. We introduce the definition of data rank in high-dimensional space, and construct rank-based high-dimensional independence test statistics; 4. According to Minimum Spanning Tree (MST), we construct symmetrical independence test statistics and study the theoretical and practical properties. For all the proposed statistics, we study the efficiency and application of different statistics with different correlations of two random variables, as well as with different dimensions of random varaibles and sample size.